: Naveen has a bag that contains 6 blue marbles, 3 green marbles, and 1 red marble. He will draw one marble randomly from the bag. Naveen is studying the effects of adding and removing marbles from the bag. Write a number in each blank to correctly complete the statements. If Naveen wants to make sure that drawing a red marble is equally likely as drawing a different color marble, then he could add

If Naveen wants to make sure that drawing a red marble is equally likely as drawing a different color marble, then he could add ***8 red marbles to the bag***

Step-by-step explanation:

The bag that contains 6 blue marbles, 3 green marbles, and 1 red marble.

Naveen wants to make sure that drawing a red marble is equally likely as drawing a different color marble, then he could add what?

Current total number of marbles = 10

Probability of drawing a red marble = (1/10)

Probability of drawing marble of other colour = (9/10)

And we want the the probability of drawing a red marble and one of the other marble to be the same.

This means we have to add a number of red marbles.

Let the number of red marbles to be added be n.

After adding n red marbles, the probability of drawing a red marble = (n+1)/(10+n)

Probability of drawing one of the other marbles = 9/(10+n)

And the probabilities are equal

(n+1)/(10+n) = 9/(10+n)

n+1 = 9

n = 9 - 1 = 8

This makes the number of red marbles 9 and total number of marbles 18.

The probability of drawing a red marble becomes (9/18) = 0.5

Probability of drawing a marble of other colour = (9/18) = 0.5 also.

to find the total number of combinations, multiply the quantity of each item by each other:

2 pairs of shoes x 3 pairs of shorts = 6 different combinations.